Thesis V1.0 Gima Msc 3d Topological Structure Management within a Dbms Validating a Topological Volume

The goal of this research is to develop a 3D topological structure with validation functionality and a conversion function. Based on this research question, some sub questions have been defined and a research methodology. The outline of this research is elaborated in chapter 1. The first use of topology has been attributed to Euler in 1736, since then, topology has evolved in mathematics but also in GIS. Since the second half of the 20 th century, 2D topological data structures are historically well established, with structures like TIGER and GBF/DIME. Several 3D topological structures have been developed as well. Most of them by researchers (for example 3D FDS and SSS). No commercial geo-DBMS has implemented a 3D topological structure, until recently. 1Spatial has developed a 3D topological structure. This structure has been analyzed among other 2D and 3D structures (chapter 2). It is clear that the existing structures differ a lot. Some structures maintain a 3D primitive while others do not. Orientation is stored in different ways, the same applies for geometry and singularities. Some structures have quite some redundancy, while other structures have only a few relationships stored explicitly, which makes maintaining the structure harder. In spite of the many differences, the characteristics of, both 2D and 3D, topological structures are based on the same aspects: dimension, partition (including the universe), primitives (including their relationships), orientation, singularities and geometrical realization. Based on these main aspects, the requirements for the topological structure are defined in chapter 3 and a conceptual model is designed. The model consist of four primitives, which are related to each other by their (co)boundary relationships. These boundary relationships exact a full space partition, where every primitive involved, is part of a volume primitive. No isolated and dangling primitives are allowed. Next to the boundaries, especially the rings and the shells, orientation plays an important role within a topological structure and the geometrical realization. Single geometries have their advantages, therefore single geometries and topological structures should be used together. Once the structure has been defined, validation rules need to be set. In order to validate a 3D topological structure, the involved volumes must be valid as well as the whole structure, which means the relationships between the volumes. Since no single definition of a valid 3D primitive is available, the rules are based on a few existing validation functions for 3D single geometries. No 3D topological validation …